资产定价因子序列相关检验
薛英杰 / 2024-02-05
因子自相关性检验
向量自回归模型如下：
\[ MKT_t=\alpha_1+\beta_{11}MKT_{t-1}+\beta_{12}SMB_{t-1}+\beta_{13}HML_{t-1}+\beta_{14}CMA_{t-1}+\beta_{15}RMW_{t-1}+\epsilon_1\\ SMB_t=\alpha_2+\beta_{21}MKT_{t-1}+\beta_{22}SMB_{t-1}+\beta_{23}HML_{t-1}+\beta_{24}CMA_{t-1}+\beta_{25}RMW_{t-1}+\epsilon_2\\ HML_t=\alpha_3+\beta_{31}MKT_{t-1}+\beta_{32}SMB_{t-1}+\beta_{33}HML_{t-1}+\beta_{34}CMA_{t-1}+\beta_{35}RMW_{t-1}+\epsilon_3\\ CMA_t=\alpha_4+\beta_{41}MKT_{t-1}+\beta_{42}SMB_{t-1}+\beta_{43}HML_{t-1}+\beta_{44}CMA_{t-1}+\beta_{45}RMW_{t-1}+\epsilon_4\\ RMW_t=\alpha_5+\beta_{51}MKT_{t-1}+\beta_{52}SMB_{t-1}+\beta_{53}HML_{t-1}+\beta_{54}CMA_{t-1}+\beta_{55}RMW_{t-1}+\epsilon_5 \]
pacman::p_load(AER,readxl,dynlm,vars,quantmod,scales,fGarch,dplyr)
load("D:\\Rblogdown\\content\\cn\\2024-02-05-factor-autregresion\\VAR.RData")
fama<-Famafactor|>
mutate(TradingMon=as.yearmon(TradingMon))
MKT<-ts(fama$MKT,start = c(1994,1),end = c(2023,9),frequency = 12)
SMB<-ts(fama$SMB,start = c(1994,1),end = c(2023,9),frequency = 12)
HML<-ts(fama$HML,start = c(1994,1),end = c(2023,9),frequency = 12)
CMA<-ts(fama$CMA,start = c(1994,1),end = c(2023,9),frequency = 12)
RMW<-ts(fama$RMW,start = c(1994,1),end = c(2023,9),frequency = 12)
VARdat<-window(ts.union(MKT,SMB,HML,CMA,RMW))
VAR_est=VAR(y=VARdat,p=1)
summary(VAR_est)##
## VAR Estimation Results:
## =========================
## Endogenous variables: MKT, SMB, HML, CMA, RMW
## Deterministic variables: const
## Sample size: 356
## Log Likelihood: 3404.231
## Roots of the characteristic polynomial:
## 0.1893 0.1893 0.05119 0.03509 0.03509
## Call:
## VAR(y = VARdat, p = 1)
##
##
## Estimation results for equation MKT:
## ====================================
## MKT = MKT.l1 + SMB.l1 + HML.l1 + CMA.l1 + RMW.l1 + const
##
## Estimate Std. Error t value Pr(>|t|)
## MKT.l1 0.042835 0.059319 0.722 0.47071
## SMB.l1 -0.403571 0.147453 -2.737 0.00652 **
## HML.l1 -0.309570 0.228101 -1.357 0.17560
## CMA.l1 -0.250213 0.212329 -1.178 0.23943
## RMW.l1 -0.618601 0.254041 -2.435 0.01539 *
## const 0.011194 0.005453 2.053 0.04083 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 0.1004 on 350 degrees of freedom
## Multiple R-Squared: 0.03567, Adjusted R-squared: 0.0219
## F-statistic: 2.589 on 5 and 350 DF, p-value: 0.02565
##
##
## Estimation results for equation SMB:
## ====================================
## SMB = MKT.l1 + SMB.l1 + HML.l1 + CMA.l1 + RMW.l1 + const
##
## Estimate Std. Error t value Pr(>|t|)
## MKT.l1 0.0002074 0.0281070 0.007 0.99412
## SMB.l1 -0.0105199 0.0698670 -0.151 0.88040
## HML.l1 -0.3444600 0.1080804 -3.187 0.00157 **
## CMA.l1 0.2389761 0.1006073 2.375 0.01807 *
## RMW.l1 0.0278996 0.1203713 0.232 0.81684
## const 0.0079815 0.0025837 3.089 0.00217 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 0.04758 on 350 degrees of freedom
## Multiple R-Squared: 0.04306, Adjusted R-squared: 0.02939
## F-statistic: 3.15 on 5 and 350 DF, p-value: 0.008532
##
##
## Estimation results for equation HML:
## ====================================
## HML = MKT.l1 + SMB.l1 + HML.l1 + CMA.l1 + RMW.l1 + const
##
## Estimate Std. Error t value Pr(>|t|)
## MKT.l1 -0.009590 0.015404 -0.623 0.534
## SMB.l1 -0.027933 0.038291 -0.730 0.466
## HML.l1 0.001731 0.059234 0.029 0.977
## CMA.l1 0.093732 0.055138 1.700 0.090 .
## RMW.l1 -0.035270 0.065970 -0.535 0.593
## const 0.001449 0.001416 1.023 0.307
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 0.02608 on 350 degrees of freedom
## Multiple R-Squared: 0.01158, Adjusted R-squared: -0.002538
## F-statistic: 0.8202 on 5 and 350 DF, p-value: 0.5359
##
##
## Estimation results for equation CMA:
## ====================================
## CMA = MKT.l1 + SMB.l1 + HML.l1 + CMA.l1 + RMW.l1 + const
##
## Estimate Std. Error t value Pr(>|t|)
## MKT.l1 -0.006086 0.018608 -0.327 0.74380
## SMB.l1 -0.073182 0.046254 -1.582 0.11451
## HML.l1 -0.079912 0.071552 -1.117 0.26483
## CMA.l1 0.192539 0.066605 2.891 0.00408 **
## RMW.l1 -0.142425 0.079689 -1.787 0.07476 .
## const 0.002986 0.001710 1.746 0.08171 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 0.0315 on 350 degrees of freedom
## Multiple R-Squared: 0.03997, Adjusted R-squared: 0.02626
## F-statistic: 2.914 on 5 and 350 DF, p-value: 0.0136
##
##
## Estimation results for equation RMW:
## ====================================
## RMW = MKT.l1 + SMB.l1 + HML.l1 + CMA.l1 + RMW.l1 + const
##
## Estimate Std. Error t value Pr(>|t|)
## MKT.l1 -0.014404 0.015324 -0.940 0.348
## SMB.l1 0.030230 0.038092 0.794 0.428
## HML.l1 0.095813 0.058926 1.626 0.105
## CMA.l1 -0.054469 0.054852 -0.993 0.321
## RMW.l1 0.105589 0.065628 1.609 0.109
## const -0.001144 0.001409 -0.812 0.417
##
##
## Residual standard error: 0.02594 on 350 degrees of freedom
## Multiple R-Squared: 0.0251, Adjusted R-squared: 0.01118
## F-statistic: 1.803 on 5 and 350 DF, p-value: 0.1116
##
##
##
## Covariance matrix of residuals:
## MKT SMB HML CMA RMW
## MKT 1.008e-02 0.0009944 -3.129e-05 0.0014764 -3.922e-04
## SMB 9.944e-04 0.0022641 -3.473e-04 0.0005074 -6.999e-04
## HML -3.129e-05 -0.0003473 6.801e-04 0.0001830 1.178e-05
## CMA 1.476e-03 0.0005074 1.830e-04 0.0009923 -2.543e-04
## RMW -3.922e-04 -0.0006999 1.178e-05 -0.0002543 6.730e-04
##
## Correlation matrix of residuals:
## MKT SMB HML CMA RMW
## MKT 1.00000 0.2081 -0.01195 0.4667 -0.15054
## SMB 0.20810 1.0000 -0.27990 0.3385 -0.56699
## HML -0.01195 -0.2799 1.00000 0.2228 0.01741
## CMA 0.46672 0.3385 0.22281 1.0000 -0.31120
## RMW -0.15054 -0.5670 0.01741 -0.3112 1.00000